C DTEA 10
C ..................................................................DTEA 20
C DTEA 30
C SUBROUTINE DTEAS DTEA 40
C DTEA 50
C PURPOSE DTEA 60
C CALCULATE THE LIMIT OF A GIVEN SEQUENCE BY MEANS OF THE DTEA 70
C EPSILON-ALGORITHM. DTEA 80
C DTEA 90
C USAGE DTEA 100
C CALL DTEAS(X,N,FIN,EPS,IER) DTEA 110
C DTEA 120
C DESCRIPTION OF PARAMETERS DTEA 130
C X - DOUBLE PRECISION VECTOR WHOSE COMPONENTS ARE TERMS DTEA 140
C OF THE GIVEN SEQUENCE. ON RETURN THE COMPONENTS OF DTEA 150
C VECTOR X ARE DESTROYED. DTEA 160
C N - DIMENSION OF INPUT VECTOR X. DTEA 170
C FIN - RESULTANT SCALAR IN DOUBLE PRECISION CONTAINING ON DTEA 180
C RETURN THE LIMIT OF THE GIVEN SEQUENCE. DTEA 190
C EPS - SINGLE PRECISION INPUT VALUE, WHICH SPECIFIES THE DTEA 200
C UPPER BOUND OF THE RELATIVE (ABSOLUTE) ERROR IF THEDTEA 210
C COMPONENTS OF X ARE ABSOLUTELY GREATER (LESS) THAN DTEA 220
C ONE. DTEA 230
C CALCULATION IS TERMINATED AS SOON AS THREE TIMES INDTEA 240
C SUCCESSION THE RELATIVE (ABSOLUTE) DIFFERENCE DTEA 250
C BETWEEN NEIGHBOURING TERMS IS NOT GREATER THAN EPS.DTEA 260
C IER - RESULTANT ERROR PARAMETER CODED IN THE FOLLOWING DTEA 270
C FORM DTEA 280
C IER=0 - NO ERROR DTEA 290
C IER=1 - REQUIRED ACCURACY NOT REACHED WITH DTEA 300
C MAXIMAL NUMBER OF ITERATIONS DTEA 310
C IER=-1 - INTEGER N IS LESS THAN TEN. DTEA 320
C DTEA 330
C REMARKS DTEA 340
C NO ACTION BESIDES ERROR MESSAGE IN CASE N LESS THAN TEN. DTEA 350
C THE CHARACTER OF THE GIVEN INFINITE SEQUENCE MUST BE DTEA 360
C RECOGNIZABLE BY THOSE N COMPONENTS OF THE INPUT VECTOR X. DTEA 370
C DTEA 380
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DTEA 390
C NONE DTEA 400
C DTEA 410
C METHOD DTEA 420
C THE CONVERGENCE OF THE GIVEN SEQUENCE IS ACCELERATED BY DTEA 430
C MEANS OF THE E(2)-TRANSFORMATION, USED IN AN ITERATIVE WAY. DTEA 440
C FOR REFERENCE, SEE DTEA 450
C ALGORITHM 215,SHANKS, CACM 1963, NO. 11, PP. 662. AND DTEA 460
C P. WYNN, SINGULAR RULES FOR CERTAIN NON-LINEAR ALGORITHMS DTEA 470
C BIT VOL. 3, 1963, PP. 175-195. DTEA 480
C DTEA 490
C ..................................................................DTEA 500
C DTEA 510
SUBROUTINE DTEAS(X,N,FIN,EPS,IER) DTEA 520
C DTEA 530
DIMENSION X(1) DTEA 540
DOUBLE PRECISION X,FIN,W1,W2,W3,W4,W5,W6,W7,T DTEA 550
C DTEA 560
C TEST ON WRONG INPUT PARAMETER N DTEA 570
C DTEA 580
NEW=N DTEA 590
IF(NEW-10)1,2,2 DTEA 600
1 IER=-1 DTEA 610
RETURN DTEA 620
C DTEA 630
C CALCULATE INITIAL VALUES FOR THE EPSILON ARRAY DTEA 640
C DTEA 650
2 ISW1=0 DTEA 660
ISW2=0 DTEA 670
W1=1.D38 DTEA 680
W7=X(4)-X(3) DTEA 690
IF(W7)3,4,3 DTEA 700
3 W1=1.D0/W7 DTEA 710
C DTEA 720
4 W5=1.D38 DTEA 730
W7=X(2)-X(1) DTEA 740
IF(W7)5,6,5 DTEA 750
5 W5=1.D0/W7 DTEA 760
C DTEA 770
6 W4=X(3)-X(2) DTEA 780
IF(W4)9,7,9 DTEA 790
7 W4=1.D38 DTEA 800
T=X(2) DTEA 810
W2=X(3) DTEA 820
8 W3=1.D38 DTEA 830
GO TO 17 DTEA 840
C DTEA 850
9 W4=1.D0/W4 DTEA 860
C DTEA 870
T=1.D38 DTEA 880
W7=W4-W5 DTEA 890
IF(W7)10,11,10 DTEA 900
10 T=X(2)+1.D0/W7 DTEA 910
C DTEA 920
11 W2=W1-W4 DTEA 930
IF(W2)15,12,15 DTEA 940
12 W2=1.D38 DTEA 950
IF(T-1.D38)13,14,14 DTEA 960
13 ISW2=1 DTEA 970
14 W3=W4 DTEA 980
GO TO 17 DTEA 990
C DTEA1000
15 W2=X(3)+1.D0/W2 DTEA1010
W7=W2-T DTEA1020
IF(W7)16,8,16 DTEA1030
16 W3=W4+1.D0/W7 DTEA1040
C DTEA1050
17 ISW1=ISW2 DTEA1060
ISW2=0 DTEA1070
IMIN=4 DTEA1080
C DTEA1090
C CALCULATE DIAGONALS OF THE EPSILON ARRAY IN A DO-LOOP DTEA1100
C DTEA1110
DO 40 I=5,NEW DTEA1120
IAUS=I-IMIN DTEA1130
W4=1.D38 DTEA1140
W5=X(I-1) DTEA1150
W7=X(I)-X(I-1) DTEA1160
IF(W7)18,24,18 DTEA1170
18 W4=1.D0/W7 DTEA1180
C DTEA1190
IF(W1-1.D38)19,25,25 DTEA1200
19 W6=W4-W1 DTEA1210
C DTEA1220
C TEST FOR NECESSITY OF A SINGULAR RULE DTEA1230
C DTEA1240
IF(DABS(W6)-DABS(W4)*1.D-12)20,20,22 DTEA1250
20 ISW2=1 DTEA1260
IF(W6)22,21,22 DTEA1270
21 W5=1.D38 DTEA1280
W6=W1 DTEA1290
IF(W2-1.D38)28,26,26 DTEA1300
22 W5=X(I-1)+1.D0/W6 DTEA1310
C DTEA1320
C FIRST TEST FOR LOSS OF SIGNIFICANCE DTEA1330
C DTEA1340
IF(DABS(W5)-DABS(X(I-1))*1.D-10)23,24,24 DTEA1350
23 IF(W5)36,24,36 DTEA1360
C DTEA1370
24 W7=W5-W2 DTEA1380
IF(W7)27,25,27 DTEA1390
25 W6=1.D38 DTEA1400
26 ISW2=0 DTEA1410
X(IAUS)=W2 DTEA1420
GO TO 37 DTEA1430
27 W6=W1+1.D0/W7 DTEA1440
28 IF(ISW1-1)33,29,29 DTEA1450
C DTEA1460
C CALCULATE X(IAUS) WITH HELP OF SINGULAR RULE DTEA1470
C DTEA1480
29 IF(W2-1.D38)30,32,32 DTEA1490
30 W7=W5/(W2-W5)+T/(W2-T)+X(I-2)/(X(I-2)-W2) DTEA1500
IF(1.D0+W7)31,38,31 DTEA1510
31 X(IAUS)=W7*W2/(1.D0+W7) DTEA1520
GO TO 39 DTEA1530
C DTEA1540
32 X(IAUS)=W5+T-X(I-2) DTEA1550
GO TO 39 DTEA1560
C DTEA1570
33 W7=W6-W3 DTEA1580
IF(W7)34,38,34 DTEA1590
34 X(IAUS)=W2+1.D0/W7 DTEA1600
C DTEA1610
C SECOND TEST FOR LOSS OF SIGNIFICANCE DTEA1620
C DTEA1630
IF(DABS(X(IAUS))-DABS(W2)*1.D-10)35,37,37 DTEA1640
35 IF(X(IAUS))36,37,36 DTEA1650
C DTEA1660
36 NEW=IAUS-1 DTEA1670
ISW2=0 DTEA1680
GO TO 41 DTEA1690
C DTEA1700
37 IF(W2-1.D38)39,38,38 DTEA1710
38 X(IAUS)=1.D38 DTEA1720
IMIN=I DTEA1730
C DTEA1740
39 W1=W4 DTEA1750
T=W2 DTEA1760
W2=W5 DTEA1770
W3=W6 DTEA1780
ISW1=ISW2 DTEA1790
40 ISW2=0 DTEA1800
C DTEA1810
NEW=NEW-IMIN DTEA1820
C DTEA1830
C TEST FOR ACCURACY DTEA1840
C DTEA1850
41 IEND=NEW-1 DTEA1860
DO 47 I=1,IEND DTEA1870
HE1=DABS(X(I)-X(I+1)) DTEA1880
HE2=DABS(X(I+1)) DTEA1890
IF(HE1-EPS)44,44,42 DTEA1900
42 IF(HE2-1.)46,46,43 DTEA1910
43 IF(HE1-EPS*HE2)44,44,46 DTEA1920
44 ISW2=ISW2+1 DTEA1930
IF(3-ISW2)45,45,47 DTEA1940
45 FIN=X(I) DTEA1950
IER=0 DTEA1960
RETURN DTEA1970
C DTEA1980
46 ISW2=0 DTEA1990
47 CONTINUE DTEA2000
C DTEA2010
IF(NEW-6)48,2,2 DTEA2020
48 FIN=X(NEW) DTEA2030
IER=1 DTEA2040
RETURN DTEA2050
END DTEA2060